Nassima kihal1, Isabelle Brunette2 and Jean Meunier1

1Department of Computer Science and Operations Research (DIRO), University of Montreal2Maisonneuve-Rosemont Hospital, Department of Ophthalmology, University of Montreal

Biometrics refers to identity recognition of persons according to theirphysical or behavioral characteristics. Many physical body parts andpersonal features have been used for biometric systems: fingers,hands, feet, faces, irises, retinas, ears, teeth, veins, voices,signatures, typing styles, gaits, odors, and DNA. Person recognitionbased on biometric features has attracted more attention indesigning security system. In this paper we propose a new biometricdatabase based on corneal topography. The cornea is the outertransparent part of the eye, and covers nearly a fifth of the eyeballsurface, with an average diameter of 11 mm (see Figure 1). Cornealtopography is a non-invasive medical imaging technique to assessthe shape of the cornea in ophthalmology. Figure 2 shows typicalcorneal topographies (images) of the anterior surface elevation from2 different subjects. These images (a.k.a. elevation maps) show themeasured height with respect to a reference (best-fit) sphere withpseudo-colors where warm colors depict points higher than thesphere and cool colors correspond to lower points. One can easilysee that these maps are different from one individual to the other(uniqueness). The idea of using this physical characteristicfor biometrics also comes from its long-term stability of many years(permanence).

Our goal is to use cornea as a new biometric trait for identityauthentication by modeling its 3D geometry. For this reason,we propose to realize a new corneal biometric database.

Materials & Methods

Figure 2: Typical topographies of 2 individuals (anterior surface elevation maps).

The database was done at the Department of Ophthalmology,Maisonneuve-Rosemont Hospital, Montreal, by using a PentacamTopographer (Oculus) see Figure 3. The Pentacam measurementprocess takes less than two seconds and minute eye movements arecaptured and corrected simultaneously. By measuring 25,000 trueelevation points, precise representation, repeatability and analysis areguaranteed. The data points are then used to generate corneal mapsused for diagnosis and treatment. Our Database contains 312 cornealtopographies captured from 39 different people of different agesusing a both eyes. For each eye, we captured two sessions of cornealtopography. The time interval between the two sessions was equalor greater than one month. In each session; 8 corneal topographies(4 left eyes end 4 right eyes) were captured. The corneal shapewas recorded as a uniformly spaced (X-Y) grid (image) of rawelevations (Z). This elevation can be represented with an appropriatemathematical model such as a Zernike polynomial expansion.

Figure 3: Pentacam Topographer Acquisition

The Zernike polynomials are a set of functions 𝑍𝑛±𝑚 𝜌,𝜃 that areorthonormal over the continuous unit circle. They have been usedextensively for phase contrast microscopy, optical aberration theory,and inter ferometric testing to fit wave-front data. These functionsare characterized by a polynomial variation in the radial direction 𝜌(for 0 ≤ 𝜌 ≤1) and a sinusoidal variation in the azimuthal direction 𝜃.The polynomials are defined mathematically by

(1)

Results & Discussion

Figure 1: Sectional view of the eyeball [National Eye Institute – NEI]

Our proposed Database was tested for person recognition.The corneal height data were decomposed into a linearcombination of the Zernike functions, we took the first 36 Zernikecoefficients as a feature vector for one cornea. To show if cornealtopography can be a good biometric alternative, two setsof comparison were processed, 741 matching comparisons (samesubjects) and 1092 non-matching-comparisons (differentsubjects) by computing the absolute difference (AD) between allZernike coefficients. Figure 4 shows the mean AD for eachcoefficient for the two tests. The more the difference betweengreen (same subjects) and red bars (different subjects) fora particular coefficient, the more this coefficient is selective fora biometric application. The figure clearly shows the potentialof Zernike coefficients for biometrics and that some coefficientsare more discriminating than others. This is also coherent withthe work of N.D. Lewis (PhD thesis 2011, U. of Arizona). In thefuture, we plan to use this database to identify the bestcombination of the most informative coefficients, e.g. with LinearDiscriminant Analysis (LDA), for biometric applications.

Figure 4: Mean difference for each Zernike coefficients within (green) and between (red) classes.

Conclusion

The objective of this work was to investigate corneal topographyas an accurate biometric modality using shape discriminatingfeatures. The results obtained confirm that corneal topographycould be an effective biometric method.

Acknowledgements

The authors would like to thank the Quebec Vision HealthResearch Network for its support.